A lot of parents use the "letting them work it out on their own method" as you described, as long as no one is getting seriously hurt. It is sometimes recommended here and is considered to fit in the realm of gentle discipline. And it can be a relief for the parents, who are generally worn out all day from negotiating conflicts.
I don't like it because I don't believe the skills to work out a conflict without resorting to power struggles, bullying, manipulating, etc come easily to younger children. I think it takes a larger view of the world to be able to see why fair and gentle negotiation is better in the long run, when tricking or sneaking or manipulating or being outright rough with your sibling works faster and the results are more immediate. Plus there seems to be something they get from the fight itself that tends to prolong the fight. Stimulation, freedom from boredom, testing wills... something. Their intent in an argument doesn't always seem to be to get what they want. It often seems to be the argument itself and maybe the feeling of winning. Lord of the Flies comes to mind when children who are age-appropriately self-centered, don't have have the bigger picture in mind, and are incapable of perceiving another person's point of view yet try to resolve conflicts without guidance.
I wish I had some good advice for how to turn it around. Everything you are doing sounds perfect and although its hard work, it will pay off in spades in a few years. Its possible you might spend a little more time teaching them to negotiate the conflict itself, although you might already be doing this (from your post it sounds like you're intervening AFTER there's problems; a little more on the other end might help. But it could also be you just didn't mention all you're doing to de-escalate before the hitting or screaming happens).
Here's some advice from NVC:
- Teach your child to use “I” messages. This can be trickier than it sounds. You want your child to learn effective “I” messages, such as “I am mad that my toy is broken,” rather than “I hate that you broke my toy!” Effective “I” messages identify what a person is feeling and why without blaming.
- Focus on the conflict at hand. When people get upset, they tend to drag in past transgressions to fuel their anger. Focus on working through only the current conflict.
- Listen. Ask kids how they suggest the conflict be resolved. Too often, parents try to intervene too quickly and take charge of the situation. Give kids the chance to work through differences. Stay close but see how far they can get peacefully talking to each other before you jump in.
- Encourage kids to admit when they’ve made a mistake. It’s important for kids to realize when they’ve done something wrong and to admit it.
- Brainstorm specific solutions. When kids are new to resolving conflicts, they often don’t know how to solve them. Sometimes having an adult name a variety of solutions can help kids begin to think of what works for them—and what doesn’t. Over time (and with practice), they’ll come up with their own creative solutions.
- Resolving conflicts peacefully is a complex skill. Notice what your child is doing right (such as calming down before trying to talk it out) rather than what he is doing wrong.
At their ages, its just going to be hard, really. Its the hardest time of all. In a few years it will get so much easier because they will already have a pretty good foundation for resolving conflicts, will be better at seeing the other person's point of view, will have developed some ability for empathy.
My brother and I (23 months apart in age) rarely fought as children. Our parents had zero tolerance for hitting, raising our voices to each other, arguing over toys, any of that. We'd either immediately lose the toy we were arguing over, get sent to separate rooms for hours, lose the TV, get spanked - my parents were firm and fairly harsh. I wouldn't recommend being that firm or harsh, and also they didn't teach us how to solve conflicts but they sure did ensure we didn't ever fight. But its also an option, if you can't stand the constant fighting and are completely worn out, to use a firmer and swifter consequence to preserve your sanity. I think this is better than allowing them to work it out on their own and develop methods of resolving conflicts that later they have to unlearn. But I think what you are doing now is probably the best approach, even though its so challenging and wears you out.